Parables can also be considered another name for moral stories. Parables are short stories that teach a moral or religious lesson. They often use simple characters and situations to convey a deeper meaning. For example, the parable of the Good Samaritan in the Bible is a well - known moral story that teaches about kindness and helping others.
A salutary story. It is a story that has a beneficial or moralizing effect. It aims to improve the reader or listener in terms of moral understanding. An example could be a story about a lazy person who learns the value of hard work through a series of events in the story, and this serves as a salutary story for those who might be lazy as well.
A short - story anthology is also a valid name. Anthology comes from the Greek words 'anthologia', which means 'a collection of flowers'. Here, the short stories are like the 'flowers' that are gathered together in one book. It's a very common term used in the literary world to describe a collection of short stories written by different authors or even by the same author.